40.A tunnel is dug along a chord of the earth at a perpendicular distance R/3 from the earth's centre. Assume that wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel.

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Q. A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R/2 from the earth's centre where R is the radius of the earth. The wall of the tunnel is frictionless.

(a) Find the gravitational force exerted by the earth on a particle of mass m placed in the tunnel at a distance x from the centre of the tunnel.

(b) Find the component of this force along the tunnel and perpendicular to the tunnel.

(e) Show that the motion of the particle in the tunnel is simple harmonic and find the time period.

Q. A tunnel is dug along a diameter of the earth. If

M_{e}

and

R_{e}

are the mass and radius of the earth respectively , then the force on a particle of mass

m

placed in the tunnel at a distance

r

from the centre is :

[Assume , walls of the tunnel are frictionless]

A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with x (distance of the particle from the centre) according to

Q. A tunnel is dug along a chord of the earth at a perpendicular distance

\frac{R}{2}

from the earth's centre. The wall of the tunnel may be assumed to be frictionless. The particle is released from the one end of the tunnel. The pressing force by the particle on the wall and the accelaration of the particle varies with

x

(distance of the particle from the centre) according to

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